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Identify the least common multiple of x^2 − 10x + 21 and x^2 − 5x − 14.

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3 votes

Answer:


(x-7)(x-3)(x+2)

Explanation:

To answer this question we factor the expressions.

For


x^2-10x +21

We are looking for 2 numbers that add up and give as a result -10 and when they multiply they give as a result 21.

These numbers are -7 and -3.

Then


x^2-10x +21 = (x-7)(x-3)

For


x^2 -5x -14

We are looking for 2 numbers that add up and give as a result -5 and when they multiply they give as a result -14.

These numbers are -7 and 2.

Then


x^2-5x -14 =(x-7)(x+2)

Finally the minimum common multiple is the common and not common factors with its greatest exponent


(x-7)(x+2)(x-3)

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